Systems and Methods for Enhancing Energy Storage in Quantum Thermodynamic Systems

ABSTRACT

In some embodiments, a device for harvesting energy from an environment energy system comprises a pump, and a coherence capacitor of metamaterial configured to store of coherence in interactions between elements of the metamaterial, a carrier fluid of particles that flushes coherence from the metamaterial and carries the coherence to a quantum heat engine via a circuit at a rate determined by a pump. The quantum heat engine is configured to harvest heat energy from the environment and use the heat energy to output useful energy while expelling waste heat back into the same environment.

BACKGROUND

Innovative approaches to portable energy sources are continually being sought since various portable electronic devices operate on portable energy sources such as batteries. The energy output of state-of-the-art (SOA) battery technologies, such as the Lithium-Sulfur Dioxide (LiSO2) primary and Lithium-ion (Li-ion) secondary systems, fall short of their projected energy capacity under load, limiting run time of electronic systems to as little as 20% of theoretical capability.

An energy storage device typically requires an energy source (one terminal of a battery) and an energy sink (the other terminal of the battery). One way to think about the inefficiencies of current battery technology is that the imputed energy difference between the source and the sink has deteriorated to so small a value that useful performance of the battery is no longer possible. This operational inefficiency can increase the number of batteries used for operation. Often, the batteries run low at critical phases of operation. Swapping old batteries for new can be cumbersome, and carrying extra batteries adds unwanted weight to luggage and other travel gear. While rechargeable batteries are available, a power source to recharge the batteries may not be available when needed.

Beginning with the 1867 postulations of James Clerk Maxwell about the possibility of a microscopic sorting demon able to work around the second law of thermodynamics, a cross-disciplinary field of research has emerged examining the relationship between the energy and the information sciences. The role of statistics and probability theory plays in underlying this relationship was highlighted with the 20^(th) century discovery and subsequent evolution of quantum theory. The quantum theoretical relationship between energy and information was more sharply adumbrated in papers by Nyquist, Hartley and finally in Leo Szilard's 1929 paper establishing the relationship between entropy and information which laid the foundations for modern cybernetics. Many important studies followed on Szilard's work until in 1961 Rolf Landauer made the discovery that erasure of information from a computer memory must dissipate a quanta of energy into the environment. Landauer's discovery has come to be called was Landauer's Principle and is one of the modern formulations of the second law. A review of this topic within the history of modern physics can be found in the works of Harvey Leif and Andrew Rex especially their jointly edited anthologies on the subject entitled “Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing”, (Institute of Physics Publishing 2003).

The subtle and profound relationships between information, entropy and energy underlying Landauer's Principle imply that systems which store information can be used in lieu of a store of energy for many of the same purposes one uses a battery, capacitor, or other energy storage device. That is, if erasing information must dissipate energy or entropy into the environment, such erasure can be used in lieu of a sink of energy or entropy to establish a flow from a source of energy. Once energy or entropy can be made to flow, useful work can be mined from that flow. Over the years since Landauer's discoveries, several classes of implementations of means to convert information erasure processes into useful work have been described in the literature, the most notable of which appeared in a series of papers in 2003 by Marfan Scully. (See Scully et al., “Using quantum erasure to exorcize Maxwell's demon: I. Concepts and context” and “II. Analysis”, and “III. Implementation” (Physica E 29 (2005) 29 if).

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments disclosed herein may be better understood, and their numerous objects, features, and advantages made apparent to those skilled in the art by referencing the accompanying drawings. The use of the same reference symbols in different drawings indicates similar or identical items.

FIG. 1A is a diagram of an embodiment of an energy system in accordance with the present invention.

FIG. 1B is a diagram of another embodiment of an energy system in accordance with the present invention.

FIG. 2A shows an example of a complete graph, representing a structure of a metamaterial that can be used in the coherence capacitor of FIGS. 1A and 1B, in which every pair of distinct nodes is connected by an edge.

FIG. 2B shows an example of the graph of FIG. 2A with disconnected edges.

FIG. 3 is a flow chart of an embodiment of a method for mining coherence from the environment enabled by the energy systems of FIGS. 1A and 1B in accordance with the present invention.

DETAILED DESCRIPTION OF THE FIGURES

Systems and methods of coherence mining with stored information disclosed herein overcome customary limits on energy storage in electrochemical devices (and some other storage concepts as well) by using both classical and non-classical phenomena from quantum and classical physics to enhance coherence storage and/or extraction. In electrochemical energy storage, the energy that is theoretically available is proportional to the mass, which means the specific performance (e.g., accessible energy per unit mass) is a fixed constant. The energy that is actually accessible is subject to various degradation and saturation effects.

Unlike batteries and electrical capacitors, in coherence capacitor energy systems described herein, information is stored in a metamaterial, which is a component of a ‘metamemory’. A metamemory stores information in the form of relations and interactions between the elements of the metamaterial. The metamemory is a graph or a set of nodes, each of which is material element such as an atom, a quantum dot, a micro-system, etc., connected by edges, which are an immaterial relation such as a correlation, a bond, a linkage, etc. As a consequence, the theoretical storage quantities for coherence scale proportionally to the square of the number of nodes and hence the mass of the metamemory, i.e., the specific performance increases proportionately with metamemory mass. Because the scaling is so favorable, a portion of the volume available in standard battery form factors can be replaced with one or more coherence capacitors and associated circuitry as described herein so that the net energy available from the form factor is boosted by an order of magnitude or more. For the scaling law to hold, 1) the graph's edges represent long range as well as short range interactions of the nodes making up the metamemory, for limiting coherence storage to short range interactions only would greatly reduce the number of edges realizable and thus compromise the favorable scaling law; and 2) a substantial proportion of the theoretically available edges are accessible. Note that since the theoretical number of edges is so large in any real case, “substantial” can mean something less than 1% and still provide very large storage capacity.

FIG. 1A is a diagram of an embodiment of energy system 100 in accordance with the present invention including pump 102, coherence capacitor 104, and Quantum Heat Engine (QHE) 106. The QHE 106 may be considered an idealized engine which converts elementary knowledge [one bit of information] into actual work. Once waste energy disposal is enabled by an erasure process, coherence capacitor 104 can be used to generate useful work from a single temperature uniform thermal bath on demand.

Coherence capacitor 104 can include a man-made metamaterial composed of elements that are able to shift back and forth between a first state which embodies and thus stores “coherence” (also referred to as “information”), and a second state which does not store coherence. A conceptual example is a metamaterial that could either exist in a glassy amorphous state at a somewhat elevated energy by comparison to a crystalline state at a lower energy is water, which exists in a liquid state below one temperature and transitions to a crystalline state (“ice”) above a specified temperature. Upon absorbing a very, very small amount of energy, each water molecule in the ice state can be freed from the crystalline structure, in effect erasing the bond that tied the molecule to that structure. And inversely, when a very, very small amount of energy is withdrawn from the molecule, the molecule attaches to that structure, establishing a bond. Coherence capacitor 104 can store information (analogous to a computer memory) by means of ligatures or molecular bonds such as Van der Waals forces, quantum entanglement, topological bending energies, or other suitable bond between atoms in molecules and higher-level structures defining the topology of the coherence capacitor 104.

The coherence is used in QHE 106 to, in effect, draw work from the environment. Coherence capacitor 104 can be discharged and its store of coherence depleted in the course of generating useful work from a single temperature bath 108 (also referred to as heat reservoir). Coherence capacitor 104 can be recharged by expending work from an external energy source (shown as W_(in) in FIG. 1) such as a solar cell, a chemical battery, or a hydrocarbon fuel engine, among others, to comply with the first and second laws of thermodynamics.

As used herein, the term “coherence capacitor” refers to a store of information or a memory from which classical phase coherence can be extracted. Stored coherence can be extracted from coherence capacitor 104 using bleed energy 112 from QHE 106 that is used as a seed current by pump 102. Using the water/ice analogy from above, a very small amount of heat is supplied to free up, or erase, one ligand tying one molecule to the ice crystal. Analogously, pump 102 can perform a very small amount of work required to “release” the coherence from coherence capacitor 104 and carry the coherence into QHE 106. The energy provided by pump 102 can be vanishingly small if the ligand tying the node to the graph is not strong. In some embodiments, pump 102 makes use of low energy optical seed pulses on the metamaterial of coherence capacitor 104, which acts similarly to a laser in that the metamaterial exists in one state of a two-state system and shifts to the other state when the bleed energy 112 is applied. The extraction of information in coherence capacitor 104 imposes a phase change in the bleed energy 112 that is carried into the QHE 106 as coherence via circuit 114. Just as a laser requires a population inversion of energy, coherence capacitor 104 requires a population inversion of coherence. The bleed energy 112 flowing through a conductor (whether real or virtual) in circuit 114 continues into QHE 106 where the coherence is “burned”. The bleed energy 112, after giving up its coherence to the QHE 106, may be recycled back into pump 102 and imposed on coherence capacitor 104 as required.

Energy system 100 operates under the Landauer Principle, which states that information, necessarily embodied in a physical system, is therefore essentially physical and erasing information dissipates an amount of entropy into the environment proportional to its temperature, k_(B)·T·ln2 (where k_(B) is the Boltzmann constant and T the absolute temperature). The Landauer Principle reduces to and is equivalent to the Second Law of Thermodynamics. In QHE 106, one bit of information embedded in the coherence of the bleed energy 112 is paired with each quantum of energy to be withdrawn from the source, a single temperature bath 108 (or its equivalent), and then the bit is erased. In effect the erasure temporarily raises the temperature of the energy quantum so that the door to the energy sink is opened for the energy quantum.

Energy system 100 can work even without any difference in energy level between an energy source (bleed energy 112), coherence capacitor 104 and an energy sink (QHE 106). Without such a difference (or in cases where the difference is too small to be useful), a transitory one (ΔT in FIG. 1A), is made to appear, induced upon erasure of the coherence (information) bit by Landauer's Principle, thus complying with the 2nd Law of Thermodynamics. This information-pairing technique enables extraction of energy from an electrochemical store, even as the potential difference between source and sink terminals of the device approaches zero by virtue of deterioration, saturation, or other cause, so long as the rest of the enabling conditions outlined herein are met. As disclosed herein, a significant enabling condition requires a store of information in coherence capacitor 104 that is accessible by a bleed energy 112 to augment the internal delta of QHE 106 with an induced boost from the erasure of information from coherence capacitor 104 at the time the energy harvested from the single temperature bath 108 is rejected back into that bath.

Any one or more of a number of suitable QHEs 106 can be used in system 100, such as described in Scully et al., “Using Quantum Erasure To Exorcize Maxwell's Demon: I. Concepts And Context”, Physica E 29 (2005) 29-39; and Rostovtsev, Yuri, et al., “Using Quantum Erasure To Exorcise Maxwell's Demon: II. Analysis”, Physica E 29 (2005) 40-46; Ramandeep S. Johal, “Quantum Heat Engines And Nonequilibrium Temperature”, Quant. Ph., 4394v1, September 2009; and Ye Yeo et al., “Quantum Heat Engines And Information”, Quant. Ph., 2480v1, August 2007.

FIG. 1B is a diagram of an embodiment of energy storage device 120 in accordance with the present invention including pump 102, coherence capacitor 104, and an embodiment of a Quantum Heat Engine (QHE) 126 that includes heat reservoir 128 and micro-laser cavity 130 as proposed by Marlin Scully et al. in “Using Quantum Erasure To Exorcize Maxwell's Demon: I. Concepts And Context”, Physica E 29 (2005) 29-39; and Rostovtsev, Yuri, et al., “Using Quantum Erasure To Exorcise Maxwell's Demon: II. Analysis”, Physica E 29 (2005) 40-46. The Scully QHE 126 operates by means of destructive interference to enable the energy quantum to be sunk back into the same heat reservoir 128 (“Qout” in FIG. 1B). Scully's QHE 126 is but one of several alternative devices for using coherence to develop useful work from a single temperature bath or reservoir 108 (FIG. 1A) and 128. Moreover, stores of information for such a purpose might yield energy storage approaches with very different characteristics in terms of their utility than existing systems which store only energy.

A variety of different implementations of coherence capacitor 104 from which coherence can be extracted and can be used to enable embodiments of the invention may be topologically and functionally equivalent at the thermodynamic level. Natural examples exist in biological molecules that fix radiative energy into chemical energy (photosynthesis and other photochemical processes). To achieve long term storage capability, however, the foregoing processes store energy and information together in chemical bonds that are generally not long range interactions and thus the full potential energy stored is considerably less than the maximum storable in the form of information alone in a completely loaded coherence capacitor 104 with the topology of a complete graph (FIG. 2A). Combustion, either in an engineered process such as a heat engine or a natural process as in metabolism, is a customary means of extracting energy from natural materials that also leaves the energy value of any information stored underutilized. The processes comprising embodiments of the present invention would correct that inefficiency in that both the energy and information stored can be converted into work to the maximum extent allowed by the laws of thermodynamics.

Referring to FIGS. 1A, 2A, and 2B, the structure of a material used in coherence capacitor 104 can be represented as a mathematical graph 200 embodied as a 2-phase metamaterial whose irreducible components are atoms 202 (“nodes” of the graph) and interactions such as correlations 204 (“edges” of the graph). Note that for FIGS. 2A and 2B, the reference numbers for atoms or nodes 202 a, 202 b, and 202 c are referred to collectively as “202”. Similarly, the reference numbers for interactions or edges 204 a, 204 b, and 204 c are referred to collectively as “204”.

In the mathematical field of graph theory, a “complete” graph 200 is a simple graph in which every pair of distinct nodes 202 is connected by an edge 204, as shown for example in FIG. 2A. The complete graph 200 on n nodes 202 has n(n−1)12 edges. Just as each edge represents a bit of information based on whether the edge 204 is present or missing, so each interaction between atoms of the crystal stores one bit of coherence. Because each bit of information has minimal energy value under the Landauer Principle, so the coherence storage metamaterial may be in a somewhat higher energy state when charged or loaded with coherence than when in the unloaded or discharged state depending on the type of interaction forming each edge. Hence the analogy to phase of a material such as water. The higher energy state (liquid) stores coherence and the discharged state (ice) does not store coherence. The liquid state is often thought of as being less organized, and thus containing less information than ice which is a more organized state. However, entropy and information can be viewed as opposites and the lower temperature state is the higher entropy/lower information content state as in classical thermodynamics. Coherence capacitor 104 can be designed either way: the coherent state can be higher or lower energy compared with incoherent state, so long as the entire system design including the QHE 106 is self-consistent.

Pump 102 in energy system 100 operates to connect and disconnectedges 204 between nodes 202 by injecting the bleed energy 112. The bleed energy 112 interacts with each edge node pair, withdrawing or injecting a small quantum of energy (coherence energy) and cooling or heating the pair of nodes 202 below or above the glass transition temperature to connect or disconnect an edge 204. Thus the bleed energy 112 is a two phase substance in a transportable form (e.g., a carrier fluid). The withdrawn energy can be bosons or fermions as long as there is a current flux. The coherence energy is transferred into or out of the bleed energy 112 by the interaction and transported to the QHE 106. An example of graph 200 with disconnected edges 204 a and 204 b is shown in FIG. 2B. Both erasing an edge 204 and creating an edge 204 between nodes 202, of course, can be considered erasing information (e.g., erasing a “1” to a “0”, and erasing a “0” to a “1”).

Although in some embodiments, elementary bosons can be used as the nodes 202, longer storage times are more simply achieved with more stable particles like fermions (e.g., electrons in quantum dots) or composite bosons (e.g., atoms or molecules). If such stable particles are selected for the nodes of the metamaterial, the mass required to store a single bit climbs substantially and the specific performance metric (e.g., accessible energy per unit mass of the system) falls off accordingly. For example, a metamaterial can be used whose nodes 202 are electrons that are immobilized within quantum dots or other suitable quantum confinement structure. Such a system can form a crystallizable liquid (similar to water) and thus a meta-crystal when sufficiently many interactions or edges 204 of the graph 200 are in place in accord with a preselected topology. The material transitions to an amorphous “meta-glass” state when above the glass transition temperature and some or all of the edges 204 are absent. Such a system can be designed so that it is stable in all topologies from a perfect glass with unestablished edges 204 to a perfect crystal fully loaded with established edges 204. Yet with proper coaxing from the bleed energy 112, the topology “decays” from crystal to glass by means of radiative decay of those interactions depositing their coherence (and a tiny bit of energy) into the bleed energy 112.

In general, there is only marginal benefit to up-scaling or down-scaling a conventional electrochemical or electrostatic energy device such as a battery, capacitor, or fuel cell beyond what is required to optimize “overhead” such as the weight of the frame, the volume lost to chemical and electrical passageways, electrodes, cooling passages and components, etc., and to reduce the transport distances over which the chemistry must reach. This is because the specific performance, that is, the performance per unit of requisite mass (the gross mass less overhead), is more-or-less constant regardless of scale. A hydrogen-based chemistry will produce no more than 1.23 electron volts (eV) per atom at standard temperature no matter how large the device is (subject to variation according to the Gibbs free energy equation).

A coherence capacitor 104, on the other hand, stores energy harvesting “capability” rather than “energy” per se, so specific performance of coherence capacitor 104 is based on the amount of information stored per unit of mass rather than the amount of energy stored per unit mass, as further described below. Assuming the mass of heat reservoir 108, if any, is not counted because it is part of the environment rather than the energy system 100, 120, the total information, that is, the total number of edges 204 (each representing one bit of information) scales as the square of the number of atoms where each atom is a node 202 of the graph 200. Thus, information is stored at an exponential rate as the number of nodes 202 increases. This scaling law is so robust that any macro-scale device is likely to contain many orders of magnitude of edges 204. Avogadro's number (A_(N)) (the number of elementary entities (atoms or molecules) in a mole of material) rounds to 24 orders of magnitude, so using conventional storage technology and associating 1.23 eV with each node (the energy available from interactions with hydrogen), one mole of material could, in principle, store A_(N)×1.23 eV or about 0.1 Mega-Joule (MJ). If the material were hydrogen, the specific performance would not exceed about 118 MJ/kilogram (kg). If instead we associated the Landauer energy K_(b)×T×ln(2)=0.0018 eV (at 300° Kelvin) with each and every possible edge 204 established, the total energy store would come to (A_(N)(A_(N)−1)/2)×0.018 eV or about 10²¹ MJ. Again assuming the nodes 202 were hydrogen atoms at 1 Atomic Mass Unit (AMU) each, the specific performance would amount to 10²⁴ MJ/kg. Even if the nodes 204 were quantum dots with a mass of one microgram each (very large for a quantum dot), the specific performance would reach nearly to 10⁶ MJ/kg—many orders of magnitude better than a battery, capacitor, or fuel cell.

The scaling law [n(n−1)/2] for a coherence capacitor 104 has implications for energy recovery/harvesting systems of all types with battery technology being but one application of interest. Other applications include harvesting environmental energy (e.g., the blackbody radiation of the earth), low grade waste energy sources (where it can contribute to net conservation strategies), and even harvesting energy fluctuations of the quantum vacuum, among others.

QHE 106 can be based on any of several concepts appearing in the art (see for example Ramandeep S. Johal “Quantum heat engines and nonequilibrium temperature”, Quant. Ph., 4394v1, September 2009). In a Scully QHE 126 (FIG. 1B), a microwave cavity (not shown) uses electrical power to establish a coherent superposition of two nearby lower energy levels in an atom gas. Heat reservoir 128 ensures thermal population of the atomic energy levels before the atom gas enters resonant micro-laser cavity 130. As a result of the current superposition of the two ground levels, destructive interference makes photon absorption unlikely while stimulated emission is unreduced. Consequently, the photon gas density increases, heating the radiation in laser cavity 130 beyond the temperature of heat reservoir 128. The temperature difference is then used in a process similar to a Carnot cycle to perform useful work M_(out) such as providing electrical current to an electrical circuit while expelling waste heat into heat reservoir 128. (For further explanation, see H. Link “Perspective on Coherent Power Boost” (Science v299 07Feb2003 p841 if) and Scully et al., “Using quantum erasure to exorcize Maxwell's demon: I. Concepts and context” and “II. Analysis”, and “III. Implementation” (Physica E 29 (2005) 29 ff).

In energy storage device 120, the microwave cavity used in a conventional Scully QHE to create the coherence is replaced with coherence capacitor 104. When the microwave cavity is replaced with coherence capacitor 104, the work done by the piston M_(out) is smaller than the work required to establish quantum coherence (W_(in)) and the laws of thermodynamics are not violated. When energy storage device 120 is used in battery applications, the resonant micro-laser cavity 130 maps into the battery's cathode while the external thermal bath 128 maps into the battery's anode. The temperature difference maps into the battery voltage.

The thermodynamic limits to specific performance of energy systems 100 (FIG. 1A), 120 (FIG. 1B), especially the energy-to-mass figure of merit, can be bounded by dividing the Landauer inequality through by the mass-equivalence of the particles forming the nodes and edges of the graph. From the black body equation (Wien's displacement law), the wavelength of a particle associated with a specific temperature T is fixed at

$\lambda = {\frac{b}{T} = \frac{{2.90 \cdot 10^{- 3}}\mspace{14mu} {m \cdot K}}{T}}$

which at standard temperature recovers the center wave length of earth's black body radiation, 10.6 microns. The photon equates to the small mass-equivalent of 1.3×10⁻¹⁰ Atomic Mass Units (AMU). Dividing the Landauer inequality through by the mass equivalent of the photon gives an upper limit for an atom-based first-order implementation (exclusive of any overhead items in energy systems 100, 120) of

${\frac{E}{m_{atom}} \leq {\frac{k_{b}}{m_{atom}}T\; \ln \; 2}} = {{1.25 \cdot 10^{10}}\frac{MJ}{kg}{\left( {{at}\mspace{14mu} {standard}\mspace{14mu} {temperature}} \right).}}$

For context, jet fuel is approximately 43.3 MegaJoules/kilogram (MJ/kg) (without considering oxidizer mass), hydrogen is approximately 143.0 MJ/kg (also without oxidizer), uranium burned in a light water reactor is often held to yield approximately 24×10⁶ MJ/kg, and the energy-mass identity E=mc² (the energy released in a matter-antimatter annihilation) is approximately 8.9×10¹⁰ MJ/kg. Thus, the first-order concept of energy systems 100, 120 appears to be capable of supporting the same magnitude of effective energy density as the maximum set forth in the energy-mass identity E=mc² and therefore need not add materially to the mass of a standard form factor device, such as batteries with the X590 form factor. The adjective “effective” is used because coherence capacitor 104 does not store energy. Coherence capacitor 104 only stores coherence which is used to harvest energy from the primary source (i.e., the single-temperature bath 108 (FIG. 1A), 128 (FIG. 1B)). And because the performance metric is one of “effective” rather than “direct and real” specific energy, the metric can easily match or even exceed the limit implied by Einstein's energy-mass identity in higher-order designs.

If the weight of the structure of coherence capacitor 104 and other overhead items required to make energy systems 100, 120 work are not taken into consideration, and using only interactions with the nearest neighbor, that is, without using long range interactions, the theoretical maximum performance metric for a device made from real particles (atoms, electrons, etc) falls to

${{\frac{E}{m_{electron}} \leq {\frac{k_{b}}{m_{electron}}T\; \ln \; 2}} = {{2.87 \cdot 10^{3}}\; \frac{MJ}{kg}}},$

which is still about a thousand times better than the theoretical performance of the best lithium battery known (i.e., the lithium thionyl chloride battery), and roughly 66 times better than jet fuel. The concept can be further modified by replacing the interaction elements with classical force elements like Van der Waals relations and/or other inter-dot interactions to express the graph's edges 204 with negligible or at least very little change in specific performance bounds because the new edge embodiment does not add much mass.

When given a sufficiently large graph 200 (large number of nodes 202), the number of unique edges 204 possible (each unique edge 204 represents one bit of coherence) rises to n(n−1)/2. A graph 200 with the maximum number of edges possible is called a complete graph. Analogously, coherence capacitor 104 with the maximum coherence load is referred to as a completely loaded coherence capacitor 104. Thus, the addition of coherence capacitor 104 mass to a customary battery form factor increases the specific performance of energy system 100 substantially.

The number of phase change states possible for a fully loaded node 202 is typically not less than n−1 (one less than the total number of nodes for each coherence capacitor 104). Coherence capacitors 104 can be coupled in parallel or in series just like batteries if the n² scaling law is to hold. In some implementations, scaling can be degraded provided it is greater than n−1.

When n is large, the number of states each node 202 can assume is equally large and thus the “spacing” between states (e.g., the energy distinction between states, or the spin distinctions between states) becomes smaller. The density of states becomes greater and thus nearly continuous, which mitigates in favor of spin states and entanglement states (e.g., topological states) as opposed to energy states and states of compound structures. The energy states of simpler, less dense systems are quantized and there is a limited energy range available for room temperature systems that limits the storage capacity of the coherence capacitor 104 and bars the applicability of the scaling law past a certain saturation point.

One way to fabricate the material of coherence capacitor 104 is with multiple layers of topological insulators like Bi2Se3 with each layer configured on the surface so as to form topological structures that synthesize fractal collages of individual spin particles. Examples of suitable topological insulators are described, for example, in “The Birth Of Topological Insulators” by Joel Moore, Nature, Vol. 464, Mar. 11, 2010, pp. 194-198. Such collages, also referred to as “knots”, can have any number of states at the same energy. A carrier fluid can wash through the collage material of coherence capacitor 104, picking up several bits of coherence at a time. The carrier fluid can be a spin current, which in the ideal case, need carry little energy.

Spin currents can be supported by electric charges in bleed energy 112 and driven by a potential difference imposed upon the spin current via the Hall Effect. The quantum spin Hall Effect allows the transport of bleed energy 112 to be dissipationless in some implementations (see for example, “Quantum Spin Hall Effect in Graphene,” C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005)). Pump 102 is a source of potential difference required to maintain the circulation. In an ideal dissipationless implementation, the pump 102 only need be used in the beginning of an energy harvesting cycle to start the circulation and then again at the end to stop the circulation of bleed energy 112, which is but one form of superconductivity. In any less-than-ideal implementation, circulation will be subject to some damping effects and will need to be maintained by operating pump 102 at some cost in make-up energy. However, provided the pumping cost in energy terms is less than the energy value under the Landauer Principle of the coherence pumped, net power remains available from the system 100. If the spin current is imposed on electrical charges (electrons or ions), a circuit 114 to conduct bleed energy 112 between coherence capacitor 104, QHE 106, and pump 102 can be made from an electrical conductor of metal wire, ionized gas, or ballistic conduction appliances like carbon nanotubes, etc.

Any make-up power for the pump can be supplied by an external source (not shown) or from bleeding a small amount of power from the QHE 106, such as bleed energy 112. The pump 102, because it serves to establish and control the rate of circulation of the coherence-carrying fluid, then, also regulates the power available from the system in the end: faster rates of circulation will cause the system 100 to generate more power, slower rates, less power. An automated electronic computer controller 118 can be included internal or external to pump 102. Controller 118 can execute logic instructions to regulate the flow of carrier fluid to coherence capacitor 104. Energy system 100 can also include one or more sensors (not shown) to provide feedback signals to controller 118. The controller 118 can convert the feedback signals to commands for operating pump 102.

$\frac{n \cdot \left( {n - 1} \right)}{2 \cdot n} = \left. {\frac{1}{2}\left( {n - 1} \right)}\Rightarrow{\frac{E}{m_{electron}} \leq {\frac{1}{2}{\left( {n - 1} \right) \cdot 2.87 \cdot 10^{3}}{\frac{MJ}{kg}.}}} \right.$

which increases with n, the linear scale of the device. Linear scale for coherence capacitor 104 will typically be the order of Avogadro's number, so maximum potential specific energy performance will customarily exceed the energy-mass identity (˜8.9×10¹⁰ MJ/kg) by many orders of magnitude even when the overhead from the quantum dots and substrates is included. Thus, the addition of coherence capacitor 104 mass to the form factor increasing the specific performance of energy storage system 100 substantially.

Pump 102 provides a motive means to drive the coherence-carrying current from the coherence capacitor 104 to the QHE 106 where it is used to harvest energy from the single temperature bath 108. In the embodiments where the coherence-carrying fluid is light (of optical, RF or other frequency) as in the example of the Scully QHE, the pump 102 can be a low power laser that takes the less coherent light scavenged from the QHE 106, and passes it through the coherence capacitor 104 where it absorbs additional coherence and then passes on the QHE 106. The transfer of coherence to the carrier fluid cools the metamaterial in the coherence capacitor 104 below the material's glass transition temperature and the metamaterial transitions to a “crystallized” state.

When all the elements of the metamaterial have “crystallized” and the capacitor 104 is depleted of coherence, capacitor 104 may be recharged to be used again provided the metamaterial from which it is made can transition between the two reversible states. In order to drive the coherence carrying fluid in the case where some damping effect tend to arrest the carrier fluid (i.e., the non-superconductive case), the pump 102 maintains a potential difference around the circuit 114 through which current 112 flows. If the carrier fluid is light as in the Scully case, the pump 102 can be a laser. If the carrier fluid is a current of electrons, however, the “pump” can be a replaced by any device that drives a potential difference, such as a battery, photovoltaic cell, inductive generator, or other suitable device. Because the work theoretically required of the carrier fluid is essentially nil, it need only be sufficient to overcome losses in the circuit 114 and can thus be vanishingly small if the circuit 114 material is of high quality and the system is designed so that the distance around the circuit 114 is short. Resistance can be, of course, effectively zero if the transport mechanism is electron “hopping” and the distance can be covered in a single hop or so—as is the case in biological photosynthesis. If photovoltaic or thermophotovoltaic cells are used to maintain the fluid circulation, the system becomes a “quasi-multiphoton process” where one photon is harvested to enable the harvesting of numerous others by the QHE 106.

Referring to FIGS. 1A and 3, FIG. 3 is a flow diagram of an embodiment of a method 300 for generating energy in accordance with the present invention. Process 302 can include operating a pump 102 or equivalently, establishing and maintaining a potential gradient in the coherence-carrying circuit 114 to extract coherence from a coherence capacitor 104 and transport the coherence to the QHE 106. The coherence capacitor 104 can include a metamaterial, also referred to herein as a “crystal”, that shifts between a first state that stores coherence and a second state when at least a portion of the coherence has been extracted. The coherence can be stored in the form of molecular interactions between atoms in molecules of the quantum crystal metamaterial. The interactions can be at least one of the group comprising Van der Waals forces, quantum entanglement, topological bending energies, quantum correlations, or other suitable interaction(s). There need not be an energy or mass difference between the metamaterial loaded with coherence as compared to its state when coherence has been depleted even though energy may be used to change between these two states. Pump 102 can be used to supply energy to the quantum crystal metamaterial to erase or establish interactions between the elements of the metamaterial to discharge or extract coherence. Changing the bond interactions between elements in the crystal “erases information” in accordance with the Landauer Principle and helps drive the coherence carrier fluid in circuit 114. The driving energy is recovered when the carrier fluid is delivered to the QHE 106. The amount of information or interactions that can be stored is exponentially proportional to the number of atoms or elements in the crystal, although the full theoretical capacity of k_(B) T ln(2) n(n−1)/2 may not be reached by some designs of metamaterials where some long range interactions are not feasible.

Process 304 includes transporting and supplying the coherence to a quantum heat engine via the carrier fluid. For example, when an interaction between nodes is erased in coherence capacitor 104, a transitory one appears under Landauer's Principle in accordance with principles put forth by Scully in (op. cit.). The store of information coherence in coherence capacitor 104 is available to augment the internal temperature difference of QHE 106 when information is erased. Circuit 114 can couple the coherence capacitor 104 to the QHE 106 and is maintained at approximately the same temperature (energy level) by thermal exchange between the circuit 114 and the thermal bath 108. The coherence delivered to the QHE 106 is used to boost the effective temperature with an imputed temperature of the working fluid by a quantum interferometric process; that is, by superposition of the coherence carrier fluid and the energy source current coming from the environment, Qin.

Process 306 includes producing useful work from the imputed temperature increase associated with erasure of the coherence as proposed by Landauer and embodied in several types of QHEs 106 (e.g., Scully's QHE 126 (FIG. 1B)). In some implementations, the useful work can be an electric current supplied to an electric circuit. QHE 126 in FIG. 1B is shown driving a piston to operate a simple mechanical machine as an example, but many alternatives for outputting work are also possible including thermophotovoltaic cells, quantum magnetohydrodynamic generators, thermal tunneling generators, among others. Mechanical work output by a QHE 106 can be converted into other forms of work such as electricity by well-known means (e.g., rotary or linear electric generators). Other types of QHE's 106 known in the art generate energy in the form of electrons, photons, phonons, or others forms. Embodiments disclosed herein not intended to be limited by the type of QHE selected nor the form of energy flowing from it.

Process 308 can include supplying energy to the quantum storage crystal metamaterial in coherence capacitor 104 to re-establish long and short run interactions initially or after the interactions are depleted during the interaction between at least some of the nodes of the metamaterial in coherence capacitor 104. The energy can be provided by any suitable device such as a solar cell, a chemical battery, and/or a hydrocarbon fuel engine.

Process 310, which can be required when there are losses in the coherence carrying circuit (the non-superconducting case), can include recycling bleed energy 112 from the quantum heat engine 106 into the pump 102. The devices that can be used to carry the bleed energy in order to power provide for the pump 102 can vary in accordance with the fluid carrying the coherence. If the carrier fluid is spin current supported by charge current, the current can be carried by electrical conductors. If the spin current is carried by neutral particles such as photons or phonons, the conductor would vary accordingly (e.g., light paths as in optical systems or fibers or sound paths as in acoustic conduits or wave guides). Such bleed energy can be vanishingly small or zero in the superconducting case (except when changes the rate of flow are required). Alternatively, process 310 can use an independent source of energy to pump the carrier fluid required to carry the coherence from its source in the coherence capacitor to the QHE. The type of conduit required for this circuit will depend upon the nature of coherence carrying current. If the coherence is carried by photons, the conduit could an optical fiber. If carried by photons, it could be a high thermal conductivity structure or a heat pipe, and so forth in accordance with the requirements of the design.

In some embodiments, pump 102 provides means for extracting coherence from a coherence capacitor 104. Pump 102 also determines the rate at which coherence is mined from coherence capacitor 104 and thus pump 102 can be controlled to match power output of the system to demand of the device being powered (shown as Wout in FIGS. 1A and 1B). The pump is operable to start, stop, and maintain the circulation of the coherence-carrying fluid around the circuit at constant and variable speed. Coherence capacitor 104 can include a quantum crystal that shifts between a first state that stores coherence and a second state when at least a portion of the coherence has been extracted. Coherence capacitor 104 can provide means for supplying the coherence to a quantum heat engine to produce energy for useful work. Interactions between atoms or other elements in the quantum crystal metamaterial from which the coherence capacitor is made can provide means for storing coherence in the quantum crystal. A solar cell, a chemical battery, and/or a hydrocarbon fuel engine can provide means for supplying energy to the quantum crystal metamaterial to re-establish bonds the interactions between at least some of the nodes in the metamaterial atoms.

While the present disclosure describes various embodiments, these embodiments are to be understood as illustrative and do not limit the claim scope. Many variations, modifications, additions and improvements of the described embodiments are possible. For example, those having ordinary skill in the art will readily implement the processes necessary to provide the structures and methods disclosed herein. Variations and modifications of the embodiments disclosed herein may also be made while remaining within the scope of the following claims. The functionality and combinations of functionality of the individual modules can be any appropriate functionality. In the claims, unless otherwise indicated the article “a” is to refer to “one or more than one”. 

1. A system for extracting energy from an environment, comprising: a circuit; a pump configured to circulate a carrier fluid through the circuit; a coherence-storing metamaterial coupled to receive the carrier fluid from the pump, the carrier fluid extracts coherence from the metamaterial by changing interactions between nodes in the metamaterial; and a quantum heat engine coupled to receive coherence extracted from the metamaterial, the quantum heat engine is configured to use the coherence to output useful energy while expelling waste energy by erasing one or more bits of the coherence.
 2. The system of claim 1, wherein the metamaterial is configured to shift between a first crystalline state that stores coherence and a second crystalline state which does not store coherence.
 3. The system of claim 1, wherein the interactions include at least one of the group consisting of: Van der Waals forces, quantum entanglement; and topological bending energies.
 4. The system of claim 1, further comprising: the pump is operable to start, stop, and maintain the circulation of the carrier fluid around the circuit at constant and variable speed.
 5. The system of claim 1, further comprising: energy to operate the pump is provided by the quantum heat engine.
 6. The system of claim 1, further comprising: the quantum heat engine is configured to use the coherence to output useful energy in the form of at least one of the group consisting of: electricity, mechanical energy, potential energy, and kinetic energy, while expelling waste energy generated by erasing the coherence.
 7. The system of claim 1, further comprising: the metamaterial is fabricated with at least one layer of a topological insulator.
 8. The system of claim 1, wherein: the quantum heat engine includes a micro-laser cavity coupled to the single temperature bath.
 9. The system of claim 1, wherein: the pump is configured to use recycled bleed energy from the quantum heat engine to drive the carrier fluid around the circuit and extract coherence from the metamaterial.
 10. A method comprising: operating a pump to extract coherence from a coherence capacitor, the coherence capacitor includes a metamaterial that shifts between a first state that stores coherence and a second state when at least a portion of the coherence has been extracted, wherein the coherence is absorbed and extracted by a carrier fluid that includes particles that pass through a metamaterial in the coherence capacitor and mate with interactions supported and anchored by nodes of the metamaterial; and circulating the carrier fluid to supply the coherence to a quantum heat engine; converting the coherence to heat in the quantum engine; and producing useful energy from the heat.
 11. The method of claim 10, further comprising: outputting useful energy in the form of at least one of the group consisting of: electricity, mechanical energy, potential energy, and kinetic energy, while expelling waste energy generated by erasing the coherence.
 12. The method of claim 10, further comprising: storing coherence in the form of molecular bonds between atoms in molecules of the quantum crystal.
 13. The method of claim 12, further comprising: supplying energy to the metamaterial to re-establish interactions between at least some of the nodes of the metamaterial.
 14. The method of claim 12, wherein: the interactions are at least one of the group consisting of: van der Waals forces, quantum entanglement, and topological bending energies.
 15. The method of claim 10, further comprising: supplying the energy to the metamaterial to re-establish bonds between at least some of the nodes of the metamaterial using at least one of the group comprising: a solar cell, a chemical battery, and a hydrocarbon fuel engine.
 16. The method of claim 10, further comprising: supplying energy from the pump to the metamaterial to disconnect at least one of the interactions between the nodes to mine the coherence.
 17. The method of claim 10, further comprising: recycling bleed energy from the quantum heat engine in the pump.
 18. An apparatus comprising: a pump; a coherence capacitor of metamaterial configured to store coherence in interactions between elements of the metamaterial; a carrier fluid circulated by the pump through the metamaterial to extract coherence from the metamaterial by changing interactions between nodes in the metamaterial; and a quantum heat engine configured to receive the coherence via the carrier fluid and to output useful energy while expelling waste heat back into the same environment.
 19. The apparatus of claim 18, further comprising: the metamaterial is configured to shift between a first crystalline state that stores coherence and a second crystalline state which does not store coherence.
 20. The apparatus of claim 18, further comprising: means for supplying energy to the metamaterial to connect interactions between at least some of the nodes. 